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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA - F. Delebecque
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
function Aclosed=h_cl(P,r,K)
//[Aclosed]=h_cl(P,r,K)
//Given the standard plant P (with r=size(P22)) and the controller
//K (computed e.g. by h_inf) this macro returns the closed loop
//matrix Aclosed whose poles allows to checks the internal stability
//of the closed loop system.
//Aclosed is the A matrix of [I -P22;-K I]^-1;
//!
if and(typeof(P)<>["rational","state-space"]) then
error(msprintf(gettext("%s: Wrong type for input argument #%d: Linear state space or a transfer function expected.\n"),"h_cl",1))
end
if typeof(P)=="rational" then P=tf2ss(P);end
[LHS,RHS]=argn(0);
if RHS==2 then //h_cl(P,K)
K=r;[A,B2,C2,D22]=abcd(P);
iK=2
elseif RHS==3 then //h_cl(P,r,K)
if typeof(r)<>"constant"|~isreal(r) then
error(msprintf(gettext("%s: Wrong type for argument #%d: Real vector expected.\n"),"h_cl",2))
end
if size(r,"*")<>2 then
error(msprintf(gettext("%s: Wrong size for input argument #%d: %d expected.\n"),"h_cl",2,2))
end
r=int(r);
if or(r<=0) then
error(msprintf(gettext("%s: Wrong values for input argument #%d: Elements must be positive.\n"),"h_cl",2,2))
end
[A,B1,B2,C1,C2,D11,D12,D21,D22]=smga(P,r);
iK=3
end
if and(typeof(K)<>["rational","state-space"]) then
error(msprintf(gettext("%s: Wrong type for input argument #%d: Linear state space or a transfer function expected.\n"),"h_cl",iK))
end
if typeof(K)=="rational" then K=tf2ss(K);end
[Ac,Bc,Cc,Dc]=abcd(K);
[n,pp]=size(B2);[ndc1,ndc2]=size(Dc);[nd1,nd2]=size(D22);
[m,q]=size(Bc);
Bw=[B2,0*ones(n,ndc2);
0*ones(m,pp),Bc];
[n1,m2]=size(Cc);
[n2,m1]=size(C2);
Cw=[0*ones(ndc1,m1),Cc;
C2,0*ones(n2,m2)];
Aclosed=[A, 0*ones(n,m);
0*ones(m,n),Ac]+...
Bw*inv([eye(ndc1,ndc1),-Dc;-D22,eye(nd1,nd1)])*Cw;
endfunction
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